Question

Convert the following repeating decimal to a fraction in simplest form. .78

Answer 1

Answer:

78/100

Step-by-step explanation:

Since .78 is in the hundredths place just move the decimal two places to the right then put it over 100. But idk if you mistyped this because .78 is not a repeating decimal

Answer 2

Answer:

6/9

Step-by-step explanation:

Change 0.7878 to a fraction.

Let n = 0.7878... Multiply both sides by 100 (by 100 when there are two repeating decimal digits)

100n = 78.7878... Subtract n from 100n.

99n = 78 Divide both sides by 99

n = 78/99 but n is 0.7878..., so

0.7878... = 78/99

Similarly with 0.66...

Let n = 0.66... Multiply both sides by 10 (by 10 when there is only one repeating digit)

10n = 6.66... Subtract n from 10n.

9n = 6 Divide both sides by 9.

n = 6/9 but n is 0.66..., so

0.66... = 6/9